402930: GYM100952 G The jar of divisors

Alice and Bob play the following game. They choose a number N to play with. The rules are as follows:

- They write each number from 1 to N on a paper and put all these papers in a jar.

- Alice plays first, and the two players alternate.

- In his/her turn, a player can select any available number M and remove its divisors including M.

- The person who cannot make a move in his/her turn wins the game.

Assuming both players play optimally, you are asked the following question: who wins the game?

The first line contains the number of test cases T (1  ≤  T  ≤  20). Each of the next T lines contains an integer (1  ≤  N  ≤  1,000,000,000).

Output T lines, one for each test case, containing Alice if Alice wins the game, or Bob otherwise.

2
5
1

Alice
Bob